An electric dipole of moment `vec(P)` is lying along a uniform electric field `vec(E )`. The work done in rotating the dipole by `90^(@)` is:

Options

A. `sqrt(2)pE`
B. `(pE)/(2)`
C. `2pE`
D. `pE`

Answer

d

Explanation

When a electric dipole is placed in an electric field `vec(E )`, a torque `vec(tau)= vec(P)xxvec(E )` acts on it. This torque tries to rotate the dipole through an angle.
If the dipole is rotated from an angle `theta_(1)` to `theta_(2)`, then work done by external force is given by
`W= pE(cos theta_(1)-cos theta_(2))`....(i)
Putting `theta_(1)= 0^(@)= 90^(@)` in Eq. (i), we get
`W= pE(cos 0^(@)-cos 90^(@))`
`= pE(1-0)= pE`